When you arrive, turn to your right and look in the nook to see another sphere containing 50 Gil . Turn around and confront the Wardens ahead of you. Smite them down and continue on your way into an event encounter. The game teaches you about using Items during battle, knowledge of which will come in handy shortly. Run to the edge of the path for a scene.
Turn back afterwards to face another group of PSICOM forces. This is probably the first battle where there is a real chance one of your characters could get knocked out. Remembering what the tutorial taught you, make judicious use of the Potions in your inventory if you need to. A nearby platform offers an escape route out of here so leap atop it and activate the controls to proceed.